Following [1]}, [2]}, one can rewrite the magnetic quadrupole coupling appearing in Eq.(REF ) in d-dimensions, by specifying the magnetic component of the Riemann tensor defined in Eq.(), and by making the following substitution:
\(S_{mult}\supset -\frac{2}{3}\int dt J^{ij}B_{ij} = -\frac{1}{3}\int dt J^{ij}\epsilon _{ikl}R_{0jkl}\ \ \rightarrow \ \ -\frac{1}{3}\int \ dt J^{k|jl}R_{0jkl} \ ,\) 
